The "tradition" Thanaton was concerned with had nothing to do with the fact that the Inquisitor killed Zash, outside of the fact that it made Zash dead. According to Thanaton, when a Sith is killed by another Sith, that Sith's power base must be wiped away. Since the Inquisitor was still Zash's apprentice at the time, he was marked for death. If instead, the Inquisitor had joined Thanaton, for example, before it happened, there would've been no rivalry. And Zash similarly wasn't punished for the same way for killing Skotia because Skotia was not her master.
this is so completely wrong in every way . i am so going to sound like a total jerk (i mean more so then i inevitably end up sounding) but if you don;t understand the tradition don't try and explain it. also what the heck does your first sentence mean? it;s entirely contradictory to it's self.